Appearance of strong spin-orbit coupling (SOC) is apparent in ternary equiatomic compounds with 5$d$-electrons due to the large atomic radii of transition metals. SOC plays a significant role in the emergence of unconventional superconductivity. Here we examined the superconducting state of HfIrSi using magnetization, specific heat, zero and transverse-field (ZF/TF) muon spin relaxation/rotation ($mu$SR) measurements. Superconductivity is observed at $T_mathrm{C}$ = 3.6 K as revealed by specific heat and magnetization measurements. From the TF$-mu$SR analysis it is clear that superfluid density well described by an isotropic BCS type $s$-wave gap structure. Furthermore, from TF$-mu$SR data we have also estimated the superconducting carrier density $n_mathrm{s}$ = 6.6 $times$10$^{26}$m$^{-3}$, London penetration depth $lambda_{L}(0)$ = 259.59 nm and effective mass $m^{*}$ = 1.57 $m_{e}$. Our zero-field muon spin relaxation data indicate no clear sign of spontaneous internal field below $T_mathrm{C}$, which implies that the time-reversal symmetry is preserved in HfIrSi. Theoretical investigation suggests Hf and Ir atoms hybridize strongly along the $c$-axis of the lattice, which is responsible for the strong three-dimensionality of this system which screens the Coulomb interaction. As a result despite the presence of correlated $d$-electrons in this system, the correlation effect is weakened, promoting electron-phonon coupling to gain importance.
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